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Four dimensional conformal C-spaces

A. Rod Gover·Paul-Andi Nagy
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Abstract

We investigate the structure of conformal $C$-spaces,a class of Riemmanian manifolds which naturally arises as aconformal generalisation of the Einstein condition. A basic question is when such a structure is closed, or equivalently locally conformally Cotton. In dimension 4 we obtain a full answer to this question and also investigate the incidence of the Bach condition on this class of metrics. This is related to earlier results obtained in the Einstein-Weyl context.

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A. Rod Gover, Paul-Andi Nagy. 2007-01-18. Four dimensional conformal C-spaces. https://arxiv.org/abs/math/0701512

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